The term "Compulsory School Age" is confusing. It does not actually mean that school is compulsory during the qualifying period. It does, however, mean that the parent or guardian of a child of "compulsory school age" has a duty to provide an education (subject to section 7 of the 1996 Education Act) during that period.
Your child is of "compulsory school age" on the 1st January, 1st April or 1st September following their 5th birthday.
Children becoming 5 years old between 1st January and 31st March are of compulsory school age at the beginning of the term after 1st April.
Children becoming 5 years old between 1st April and 31st August are of compulsory school age from the beginning of the term after 1st September.
Children becoming 5 years old between 1st September and 31st December are of compulsory school age from the beginning of the term after 1st January.